簡約 (ln(1500)-ln(1500-19200))/(ln(1.03))

解

簡約

\frac{ln ( 1500 ) - ln ( 1500 - 19200 )}{ln ( 1.03 )}

\frac{ln ( - \frac{5}{59} )}{ln ( 1.03 )}

解答ステップ

\frac{ln ( 1500 ) - ln ( 1500 - 19200 )}{ln ( 1.03 )}

対数の規則を適用する:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln (1500) - ln (1500 - 19200) = ln (\frac{1500}{1500 - 19200})

= \frac{ln ( \frac{1500}{1500 - 19200} )}{ln ( 1.03 )}

\frac{1500}{1500 - 19200} = - \frac{5}{59}

= \frac{ln ( - \frac{5}{59} )}{ln ( 1.03 )}